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The key problems in applying the adaptively robust filtering to navigation are to establish an equivalent weight matrix for the measurements and a suitable adaptive factor for balancing the contributions of the measurements and the predicted state information to the state parameter estimates. In this paper, an adaptively robust filtering with classified adaptive factors was proposed, based on the principles of the adaptively robust filtering and bi-factor robust estimation for correlated observations. According to the constant velocity model of Kalman filtering, the state parameter vector was divided into two groups, namely position and velocity. The estimator of the adaptively robust filtering with classified adaptive factors was derived, and the calculation expressions of the classified adaptive factors were presented. Test results show that the adaptively robust filtering with classified adaptive factors is not only robust in controlling the measurement outliers and the kinematic state disturbing but also reasonable in balancing the contributions of the predicted position and velocity, respectively, and its filtering accuracy is superior to the adaptively robust filter with single adaptive factor based on the discrepancy of the predicted position or the predicted velocity.

The absolute positioning technique is based on a point positioning mode with a single Global Navigation Satellite System (GNSS) receiver, which has been widely used in many fields such as vehicle navigation and kinematic surveying. For a long period, this positioning technique mainly relies on a single GPS system. With the revitalization of Global Navigation Satellite System (GLONASS) constellation and two newly emerging constellations of BeiDou Navigation Satellite System (BDS) and Galileo, it is now feasible to carry out the absolute positioning with quad-constellation of GPS, GLONASS, BDS, and Galileo. A combination of multi-constellation observations can offer improved reliability, availability, and accuracy for position solutions. In this chapter, combined GPS/GLONASS/BDS/Galileo point positioning models for both traditional single point positioning (SPP) and precise point positioning (PPP) are presented, including their functional and stochastic components. The traditional SPP technique has a positioning accuracy at a meter level, whereas the PPP technique can reach an accuracy of a centimeter level. However, the later relies on the availability of precise ephemeris and needs a long convergence time. Experiments were carried out to assess the kinematic positioning performance in the two different modes. The positioning results are compared among different constellation combinations to demonstrate the advantages of quad-constellation GNSS.